Wave filter



Arifl M, 1936. 5 LANE WAVE FILTER Filed June 23, 1933 V V IN FREQUENCY FIG. 7

IN l E N TOR A T TORNE V Patented Apr. 14, 1936 WAVE FILTER Clarence E. Lane, West Orange, 'N. J assignor to Bell Telephone Laboratories,

Incorporated,

New York, N. Y., a corporation of New York Application June 23, 1933, Serial No. 677,244 20 Claims. (01. 178-44) This invention relates to wave transmission networks and more particularly to frequency selective networks, such as wave filters, which employ piezoelectric crystals as impedance elements.

An object of the invention is to reduce the cost of manufacturing wave filters employing piezoelectric crystals.

Another object is'to permit the use of thinner piezoelectric crystals in such filters.

Another object is to extend the frequency range and the impedance range over which a series of wave filters employing piezoelectric crystals may be made to function successfully.

A further object is to vary the characteristic impedance of such a filter over a wide range without materially changing the attenuation characteristic. I

A feature of the invention is the combination of a piezoelectric crystal with a capacitance connected in shunt therewith and a second capacitance connected in series, the combination being the electrical equivalent of a second thicker piezoelectric crystal shunted by a capacitance.

Another feature is a wave filter employing a plurality of piezoelectric crystals all of which have the same thickness.

Another feature is a series of such filters designed to operate over different frequency ranges, all of the component piezoelectric" crystals being of the same thickness.

Still another feature of the invention is a band filter comprising piezoelectric crystals, the characteristic impedance of which may be varied over a wide range, without material change'in the Width or location of the band, by means of variable condensers only.

The well known property of low energy dissipation in piezoelectric crystals such as quartz crystals makes them highly suitable for use as impedance elements infrequency selective networks. Such crystal elements may, for example, be combined with simple inductances and capacitances to form the branches of a lattice type Wave filter which will provide a wide transmission band, while at the same time the advantages arising from the low energy dissipation in the crystal are maintained. The length of the crystal required in'such a filter depends primarily upon the location of the frequency band to be transmitted, and in order that the crystal will vibrate in the proper mode the thickness of the crystal must be kept small relative to its length.

But, in general, the higher the characteristic impedance of the filter is made, the thicker the required crystal becomes. It follows, therefore,

that if a filter designed to pass a band of a certain width centered at a given frequency is to havea high impedance then conflicting requirements are placed upon the component crystal, namely, that its thickness shall be small in order 5 5 for the crystal'to vibrate in the desired mode, and that its thickness shall be large-in order to provide a high impedance'filter; In accordance with the present invention this difiiculty is. obviated by the'use of a crystal which is thin enough to assure the proper mode of vibration but the impedance of which is stepped up by theaddition of a capacitance in series therewith and the adjustment of the condenser which normally shunts the crystal; In this wayit is possible to build a filter having a higher characteristic impedance, orone. which will operate successfully at a higher frequency than would otherwise bepossible.

As an adaptationv 0f the invention there'is 2 a piezoelectric crystal in'each branch in which all of'the crystals are of the samethickness Also, as an extensionzof this method of construction it is-show'n how a series of band-pass filters 5 may be' built having-transmission bands spaced at-intervals along the frequency spectrum but employing crystals of uniform thickness for all of the filters. In this way the cost of manufacturing the filters is materially reduced because it is more economical to grind a number of crystals all to'the same thickness than it is to grind each crystal to a different thickness.

Thefact that the impedance of a crystal element may be stepped up by the addition of a capacitance in series therewith is also utilized in the provision of a variable impedance filter comprising only piezoelectric crystals and variable capacitances. The characteristic impedanceof "the filter may be continuously varied over 'a wide 40 range simply by varying the component capacitances' The location of the transmission band and its width remain practically unchanged. Inf this way a very useful typeof filter is provided, since its impedance may readily bev adjusted .to match .the load impedances between which, it is. to operate, and thereby eliminate reefiection efiects.

The nature of 'the invention will be more fully understood from the following detailed description and by reference to the accompanying drawing, of which: 1 Fig; 11 shows a form of piezoelectric suitablefor use in wave; filters;

Fig. 2 represents schematically a type of filter to which the invention is applicable;

Figs. 3 and 4 show combinations of crystal element, series capacitance and shunt capacitance, embodying the invention;

Fig. 5 illustrates the type of impedance characteristics obtainable with the combinations shown in Figs. 3 and 4;

Fig. 6 shows the embodiment of the invention in a lattice type section;

Fig. 7 represents the type of transmission characteristics obtainable from a series of band filter sections embodying the invention, in which crystals of uniform thickness are employed;

Fig. 8 illustrates schematically a variable impedance band filter embodying the invention;

Fig. 9 represents the equivalent electrical circuit of a piezoelectric crystal to which reference is made in explaining the invention; and

Fig. 10 shows a series of filters embodying the invention.

A form of piezoelectric crystal suitable for use in wave filters for frequencies up to about 500 kilocycles per second is shown in Fig. 1, in which Ill represents a rectangular crystal, preferably of quartz, having its length 2 parallel to the mechanical axis MM, its width to parallel to the optical axis 00" and its thickness in the direction of the electrical axis EE. Electrodes H and I2 are applied to the large faces of the crystal, that is, to the surfaces perpendicular to the electrical axis, preferably by the electrical deposition of a layer of silver or other metal to secure an intimate contact over the whole surface. Leads l3 and M are connected to the elec: trodes by soldering with soft solder or by other appropriate means. Crystals of this type when subjected to an alternating potential difference between the electrodes vibrate mainly by expansion and contraction in the direction along the mechanical axis. They should, therefore, be supported between points or knife-edge clamps such as l5 and I6, located near the center of the crystal along the optical axis.

A type of wave filter to which the invention is applicable is shown in Fig. 2. The filter comprises a symmetrical lattice each line branch of which is constituted by a piezoelectric crystal K1 in parallel with a capacitance C1, and each diagonal branch of which consists of a crystal K2 shunted by a capacitance C2, the structure being completed by the four equal inductances L connected between the terminals of the lattice section and the input terminals l1, l8 and the output terminals 19, of the filter. It is well known that the impedance elements of such a filter may be proportioned to produce a bandpass characteristic or other desired attenuation characteristic. For a detailed explanation of how this may be done reference is made to the copending applications of W. P. Mason, Serial No. 489,268, filed October 1'7, 1930 and Serial No. 653,622, filed January 26, 1933.

For frequencies up to and well above the first resonance the electrical impedance of a parallel combination of crystal and capacitance such as is shown between terminals 2| and 22 of Fig. 2, is of a simple character corresponding to that of an electrical circuit comprising a capacitance shunted by an arm consisting of an inductance and capacitancein series. The impedance of such a combination, which is practically wholly geactive has a frequency characteristic of the type shown by the solid line curve 23 of Fig. 5. At low frequencies the reactance is negative or capacitative, with the magnitude diminishing with increasing frequency to zero at a resonance frequency f1. Above this frequency the reactance becomes positive and rises rapidly to an infinite value at an anti-resonance frequency f2, above which it again becomes negative and decreases in magnitude with increasing frequency. The principal resonance frequency of the combination is determined primarily by the length l of the crystal. Other resonances, representing changes in the mode of vibration of the crystal, are practically eliminated so long as the length of the crystal is greater than its width and its thickness is relatively small. But if the characteristic impedance of the filter is to be high the crystal must be made relatively thick. This latter requirement directly conflicts with the requirement that the crystal should be kept relatively thin for vibration in the proper mode. It follows, then, that if the resonance I1 is to be placed at a certain frequency, and the filter is to have a comparatively high characteristic impedance, it will be impossible by ordinary methods to build a filter which will function satisfactorily.

In accordance with the invention, this difficulty is avoided by replacing the combination shown between terminals 2| and 22 of Fig. 2 by the combination of elements shown in Fig. 3 which comprises a thinner crystal Ka shunted by a variable capacitance C11, and in series with the combination a second variable capacitance Cb. By the proper choice of the series capacitance Cb and by the adjustment of the shunt capacitance C9. the impedance of the combination shown in Fig. 3 may be made exactly the same as the impedance of the crystal K shunted by the capacitance C1, and therefore the former combination may be substituted for the latter in the filter of Fig. 2 without affecting its impedance or transmission characteristics.

A method which may be followed in choosing the required values for the capacitances Ca and Cb will now be explained by reference to the impedance curves shown in Fig. 5, in which curve 23 represents the reactance of the crystal K1 in parallel with the capacitance C1, f1 being the resonance frequency and f2 the frequency of anti-resonance of the combination. If the crystal K1 is replaced by a thinner and slightly longer crystal K3,, having the same ratio of width to length as the replaced crystal, the shunt condenser C1 remaining unchanged, the new combination will have a somewhat lower resonance frequency is and a lower frequency of anti-resonance f4, as indicated by the full line curve 24 of Fig. 5. Now, if a variable capacitance Cb be added in series with the combination, the resonance frequency is will be raised, and by properly adjusting the value of Cb this frequency may be made to coincide with the frequency f1. At the same time, the frequency of anti-resonance will be raised from ii to some new frequency f5, as indicated by the dotted curve 25 of Fig. 5. Now, in order to make the curve 25 coincide at all points with the curve 23 it is only necessary to increase the value of the shunt capacitance C1 until the frequency of anti-resonance ft is raised to the frequency f2. For this purpose it is convenient to replace C1 by the variable capacitance Ca and adjust the latter to the required value.

Changing the value of Ca affects only the antiresonance frequency is, the resonance frequency f1 remaining undisturbed. Once the required values for Ca and Cb have been found, the variable condensers may be replaced by fixed ones, if

desired. Also, the proper values for the capacitances Ca and C11v may be determined by direct computation from equations and 4 presented below, if that method is preferred, and in that case no variable condensers are required.

It will now be explained howthe required length of the replacing crystal K& may be evaluated in terms of the physical dimensions of the replaced crystal K1, the thickness of the replacing crystal Ka and themagnitude of the capacitance C1 expressed in mioro-microfarads. For a crystal of the type shown in Fig. 1 the equivalent electrical circuit, as shown in Fig. 9, may be represented by a capacitance C11 shunted by a branch consisting of an inductance Lin and a second capacitance Cm. The capacitance C11 is the simple electrostatic capacitance between the electrodes of the crystal. The values of the inductance Lin and the capacitance Cm depend not only upon the dimensions of the crystal but also upon its piezoelectric and elastic constants. For quartz crystals of the type shown in Fig. 1 the values of the elements of the equivalent electrical circuit are given in terms of the crystal dimensions by the following equations:

L,,,= henries (1) C micro-microfarads (2) micromicrofarads (3) Where Z is the length, t the thickness, and w the width of the crystal in centimeters.

If the equivalent reactance elements of the crystal K1 are designated Lm, Cm and C11 as in Fig. 9, the value of the series capacitance C11 of Fig. 3 may be expressed as and the value of the shunting capacitance C1 is given by the equation where 251 is the thickness of the crystal K1 and i2 is the thickness of the replacing crystal Ka. The corresponding equivalent reactance elements Lin and C111 of the replacing crystal Ka may be found from the expressions 1,= arm/Lye... (9)

Substituting in Equation (9) the values of L111 and Cm given by Equations (6)and (7) gives Ig=21rk cm+cn+cl cm g Squaring Equations (8) and (10) and dividing the latter by the former gives Substituting in Equation (11) the values of Cm and C11 given by Equations (2) and (3) gives from which the length 12 of the replacing crystal Ka may be determined in terms of the capacitance C1 in micro-microfarads, the length 11, width an, and thickness t1 of the crystal K1 and the thickness t2 of the crystal Ka, all dimensions being expressed in centimeters.

If the elements K11, C11 and Ch have been proportioned as explained above then the combination shown in Fig. 3 may be substituted for the crystal K1 and capacitance C1 appearing between the terminals 2| and 22 indicated in Fig. 2. A similar combination comprising Kt, Ca. and Ch may be substituted for the other line branch of the lattice of Fig. 2. The same procedure may be followed in working out a combination comprising a crystal Kb and capacitance Cc, Cd which may be substituted for each diagonal branch of the lattice. The resulting filter, with the new branches of the lattice in place, is shown schematically in Fig. 6. The inductances L are left unchanged.

As a concrete illustration giving the physical dimensions of the crystal element and the magnitudes of the associated capacitances required in each line branch of a wave filter embodying the invention the following data are presented. In a band-pass filter of the configuration shown in Fig. 2 having a characteristic impedance of 1100 ohms, a mid-band frequency of 98280 cycles per second and a theoretical band Width of 3800 cycles per second the crystal K1 was found to have the following dimensions in millimeters:

t1: 2.767 Z1=26.724 w1=12.908

The shunting capacitance C1 had a magnitude of 52.139 micro-microfarads. In accordance with the invention, this branch of the filter may be replaced, as explained above, by an impedance branch of the form shown in Fig. 3 which em- 'ploys a crystal element having a more convenient thickness. The dimensions in millimeters of the replacing crystals K11 may, for example, be as follows:

It will be noted that, in the illustration, the thickness i2 is less than a third of the thickness t1 of the replaced crystal K1. Any other ratio of 252 to t1 less than unity could, of course, be used. For a crystal having the dimensions given above for K1 the magnitudes of the associated capacitances in micro-microfarads are found to 'be as follows:

Ca 86.442 Cb:131.380

, The combination shown in Fig, 3 may be replaced, if desired, by the equivalent circuit shown in Fig. 4, comprising a variable capacitance Cx' shunted by an arm consisting of the crystal Ky in series with a second variable capacitance Cy. The impedance of the crystal Ky will be the same at all frequencies as that ofthe crystal Ka, multiplied by a constant. The necessary relationships existingbetween the values of the reactances in the equivalent circuits are well known and are given, for example, in Transmission Circuits for Telephonic Communication, by K. S. Johnson, page 267, Equations (1), (2) and (3).

As an adaptation of the invention the crystals Kb in the diagonal branches of Fig. 6 may be chosen of the same thickness as the crystals K8. in the line branches.

As a further extension of the invention, a series of band-pass filters may be built having transmission bands placed at different frequencies, such for example, as those shown by curves 26, 21 and 28 of Fig. '7, but employing crystals of uniform thickness for all of the filters. Fig. 7.0 shows a series of three such filters F1, F2 and F3 connected in parallel to a transmission line TL. Each of the filters may have the configuration shown in Fig. 6, for example. This construction conduces to economical manufacture of the filters inasmuch as grinding a number of crystals to the same thickness by a machine lapping process is less expensive than grinding each crystalto a different thickness, which latter method generally requires tedious hand work.

Another embodiment of the invention is illustrated diagrammatically in Fig. 8, which shows a lattice type band-pass filter the characteristic impedance of which may be varied over a wide range of values simply by the manipulation of variable capacitances. It is well known how to construct a band filter of the lattice type in which each line branch and each lattice branch consists of a piezoelectric crystal elementshunted by a capacitance. For a more detailed description of the design of such a filter, reference is made to the aforementioned Mason applications. In accordance with the present invention each of the shunting capacitances is made variable, and a second capacitance is inserted in series with each branch so that its impedance level may be raised or lowered without appreciably changing the frequencies of resonance and anti-resonance, as explained above in connection with Fig. 3. Thus, each line branch of the filter shown in Fig. 8 consists of a crystal K3 shunted by a variable capacitance C3, the combination being connected in series with a second variable capacitance C4;

and each lattice branch is made up of a variable capacitance C6 in series with the parallel combination comprising the crystal K4 and the variable capacitance C5. In order to increase the impedance of the filter all of the variable capacitances, C3, C4, C5 and C6, are decreased in value; in order to decrease the filter impedance, these capacitances are increased in magnitude. The width of band transmitted by the filter will remain fixed, regardless of the impedance setting, but as the impedance is raised the mid-band frequency may increase slightly. This latter effect, however, is unimportant inmost instances.

As an example illustrating the actual values of capacitance required in a variable impedance filter of the kind described above, the following data are presented. With no series capacitances in the branches, the filter has a characteristic impedance'of 10,000 ohms and passes a 20 cycle band fcentered at 50 kilocycles per second. With the addition of series capacitance the impedance may be varied continuously from 10,000 ohms to nearly 1,000,000 ohms, the latter figure representing the condition where the capacitance in shunt with the crystal has been reduced to zero. The following table gives the values required, in micro-microfarads for the capacitances C3 and C4 of the. line branches when the characteristic impedance Zn of the filter is set, respectively, at 10,000, 20,000 and 939,700 ohms.

Zo- C3 C4 10,000 281.0 20,000 189.6 535.3

The magnitudes of the capacitances C5 and Cs associated with'the lattice branches will vary approximately in the same ratio as the corresponding capacitances in the line branches, given in the table. The crystals K3 and K4, of course, remain unaltered. When the impedance of the filter is increased from 10,000 to 20,000 ohms, the center of the transmission band is 'moved up in frequency approximately eight cycles, but this shift is of little importance when it is considered that the band is centered at 50,000 cycles. The width of the band, 20 cycles, remains unchanged as the impedance of the filter is varied.

What is claimed is:

1. In a wave transmission network of the lattice type having a pair-of input terminals and a pair of output terminals, a plurality of pairs of impedance branches connected between said input terminals and said output terminals, one of said impedance branches comprising a piezoelectric crystal as an impedance element, a capacitance shunting said'crystal anda second capacitance connected effectively in series with said crystal, said impedance branch being the electrical equivalent of a dififerent thicker crystal shunted by a capacitance.

2. A wave transmission network of the lattice type comprising a plurality of pairs of impedance branches connected between a pair of input terminals and a pair of output terminals, one of said impedance branches comprising in combination a capacitance shunted by an impedance arm comprising a second capacitance and a piezoelectric crystal element connected in series relation.

3. A wave filter comprising a plurality of pairs of impedance branches connected between a pair of input terminals and a pair of output terminals to form a lattice network, one of said impedance branches comprising a capacitance in series with a combination comprising a second capacitance and a piezoelectric crystal element connected in parallel.

4. A wave filter of the lattice type having a plurality of pairs of impedance branches connected between a pair of input terminals and a pair of output terminals, one of said impedance branches comprising avariable capacitance connected in series with a combination comprising a second variable capacitance in shunt with a piezoelectric crystal, whereby, by the adjustment of said variable capacitances, the impedance of said branch may be varied without displacing its critical frequencies. v

5. A broadband wave filter having aplurality of pairs of impedance branches connected between a pair of input terminals and a pair of output terminals to form a lattice network, one of said impedance branches comprising two capacitances connected in series, one of said capacitances being shunted by a piezoelectric crystal element, and said impedance branch being the electrical equivalent of a different thicker crystal shunted by a capacitance.

6. A wave filter comprising a plurality of impedance branches connected between a pair of input terminals and a pair of output terminals, each of said branches including two capacitances connected in series, one of said capacitances being shunted by a piezoelectric crystal element, and all of said piezoe ectric crystal elements being of the same thickness.

'7. A broad band wave filter comprising a plurality of impedance branches arranged to form a lattice network, each of said branches including a piezoelectric crystal impedance in combination with two separate capacitances, and all of said piezoelectric crystals being of the same thickness.

8. A broad band wave filter comprising a plurality of impedance branches arranged to forma lattice network, each of said branches including a piezoelectric crystal impedance, a capacitance in shunt thereto and a second capacitance in series therewith, and all of said crystals being of the same thickness.

9. A broad band wave filter comprising a plurality of impedance branches arranged to form a. lattice network, each of said branches including two capacitances and a piezoelectric crystal element in shunt with one of said capacitances, all of said crystals being of the same thickness.

10. A broad band wave filter comprising a plurality of impedance branches arranged to form a. lattice network between a pair of input terminals and a pair of output terminals, each of said branches including as impedance elements a piezoelectric crystal and two separate capacitances, one of said capacitances being connected efiectively in series with said crystal and the other of said capacitances being connected effectively in shunt with said crystal, and all of said crystals being of the same thickness.

11. A broad band wave filter comprising two pairs of similar impedance branches arranged to form a symmetrical lattice network between a pair of input terminals and a pair of output terminals, each of said branches including as an impedance element a piezoelectric crystal, all of said crystals being of the same thickness, the crystals included in one of said pairs of branches having a frequencycharacteristic different from that of the crystals in the other pair and proportioned with respect thereto to provide a single transmission band. 7

12. A lattice-type wave filter comprising a plurality of pairs of impedance branches connected between a pair of input terminals and a pair of output terminals, each of said branches including as impedance elements a piezoelectric crystal and two variable capacitances, all of said crystals being of the same thickness, and the crystals in one of said pairs of branches having a frequency characteristic difierent fromthat of the crystals in another pair of said branches and being proportioned with respect thereto to provide a single transmission band.

13. A plurality of wave transmission networks having transmission bands centered at difierent frequencies, each of said networks comprising a piezoelectric crystal as an impedance element, and all of said crystals being of the same thickness.

14. A plurality of wave filters having diverse transmission characteristics, each of said filters comprising a. plurality of impedance branches connected between a pair of input terminals and a pair of output terminals, each of said branches including a piezoelectric crystal as an impedance element, and all said crystals being of the same thickness.

15. A plurality of wave filters having different attenuation characteristics, each of said filters comprising two pairs of similar impedance branches disposed between a pair of input terminals and a pair of output terminals to form a symmetrical lattice network, each of said branches including a. piezoelectric crystal as an impedance element, and all of said crystals being of the same thickness.

16. A plurality of wave filters having transmission bands centered at different frequencies, each of said filters comprising a plurality of impedance branches arranged to form a lattice network, each o-f said branches including a piezoelectric crystal in combination with two capacitances, all of said crystals being of the same thickness.

1'7. A plurality of wave filters having transmission bands centered at difierent frequencies, each of said filters comprising a plurality of impedance branches arranged to form a lattice network, each of said branches including a piezoelectric crystal, and all of said crystals being of the same thickness.

18. A variable impedance wave filter comprising a plurality of impedance branches arranged to form a lattice network, each of said branches including a piezoelectric crystal element and a plurality of variable capacitances cooperating therewith for varying the impedance of said branches without materially changing the transmission characteristics of said filter.

19. A variable impedance wave filter comprising a plurality of impedance branches arranged to form a lattice network, each of said branches including a piezoelectric crystal impedance in combination with two variable capacitances, whereby the characteristic impedance of said filter may be varied without materially altering its attenuation characteristic.

20. A variable impedance wave filter comprising a plurality of impedance branches arranged to form a lattice network, each of said branches including a piezoelectric crystal element, a variable capacitance in shunt thereto, and a second variable capacitance in series therewith, whereby the characteristic impedance of said filter may be varied while the width and location of its transmission bands remain unaltered.

CLARENCE E. LANE. 

